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EGGPlacer: Energy-Guided Generative Chip Placement with Diffusion Models

Qi Zhou, Guojun Liu, Juanhong Zhao, Guangzhi Qi, Zehao Chen, Ming Lu

arXiv:2610.33099v1cs.ARcs.AI

TL;DR

Macro-placement metrics are difficult to evaluate before downstream placement and routing, while existing learning-based and analytical approaches expose different subsets of physical objectives. EGGPlacer injects analytical and thermal guidance into diffusion sampling; the paper reports strong combined placement, routed-wirelength, thermal, and runtime results, while noting that HPWL proxy fidelity varies across placement engines.

  • Problem

    Learning-based placers often optimize mHPWL, while analytical placers account for full-netlist wirelength and density but not temperature, leaving both signals unavailable together to macro generation.

    Source: §2 · p. 4

  • Method

    EGGPlacer injects analytical wirelength and density feedback and differentiable thermal guidance into the reverse diffusion process.

    Source: §1 · pp. 2–3

  • Results

    On 20 open-source designs, EGGPlacer achieves strong combined HPWL, routed-wirelength, thermal, and runtime results, while HPWL proxy fidelity varies across placement engines.

    Source: §1 · p. 3, §5 · pp. 9–10

  • Takeaways & Limitations

    HPWL proxies should be aligned with the target downstream flow, and calibration of physical predictors remains a promising direction.

    Source: §5 · p. 10

Abstract

from arXiv · show

Chip placement strongly affects routed wirelength and thermal behavior, yet these downstream metrics are difficult to evaluate during macro placement. Learning-based macro placers commonly optimize the macro-only half-perimeter wirelength (HPWL), denoted mHPWL, which ignores standard cell connectivity and spatial demand. In contrast, analytical mixed-size placers optimize differentiable full netlist wirelength and density objectives but are typically unaware of thermal effects. We propose EGGPlacer, an energy-guided diffusion framework that incorporates analytical placement feedback and thermal feedback into macro placement generation. An analytical placer acts as an online physical response model, exposing the standard cell distribution and a full netlist wirelength proxy induced by each intermediate macro placement, while a differentiable thermal model provides temperature feedback. These signals are formulated as composable energies and injected throughout reverse diffusion without retraining the underlying generative model. Experiments on public placement benchmarks show that EGGPlacer achieves competitive mixed-size HPWL relative to strong analytical and learning-based macro placers. In the end-to-end evaluation, EGGPlacer also obtains the lowest average routed wirelength and peak temperature among the evaluated methods. Ablation studies further demonstrate that analytical and thermal guidance provide distinct and complementary benefits across wirelength proxies, routed wirelength, and thermal objectives.

1 INTRODUCTION

EGGPlacer addresses the gap between macro-placement objectives and downstream design quality by injecting analytical and thermal feedback into diffusion sampling. The introduction highlights variation in HPWL’s fidelity as a routed-wirelength proxy across placement engines.

1 INTRODUCTION

  • Evaluating macro placements is difficult because routed wirelength, timing, power, and thermal behavior depend on later standard-cell placement, legalization, and routing.Figure 1 previews EGGPlacer’s combined routed-wirelength, peak-temperature, and runtime results.Source: §1 · p. 1, Figure 1 · p. 1
  • For circuits with hundreds of macros and many standard cells, repeated downstream evaluation is prohibitively expensive, motivating informative and inexpensive feedback during generation.Diffusion trajectories provide intervention points for injecting downstream physical feedback before the final placement is determined.Source: §1 · p. 2
  • Learning-based placers commonly optimize mHPWL, while analytical mixed-size placers account for full-netlist wirelength and density but not temperature.mHPWL omits standard-cell connectivity and spatial demand, leaving neither approach with both standard-cell-aware and thermal feedback.Source: §1 · p. 2
  • EGGPlacer injects analytical and differentiable thermal energies into reverse diffusion, exposing standard-cell-aware physical feedback and temperature changes during macro generation.Analytical guidance supplies a full-netlist wirelength proxy and density; thermal guidance supplies temperature feedback.Source: §1 · pp. 2–3
  • HPWL’s fidelity as a routed-wirelength proxy varies across placement engines, underscoring the importance of aligning macro generation with the downstream design flow.Source: §1 · p. 3

2 PROBLEM FORMULATION

Macro placement predicts the center coordinates of movable macros within geometric constraints. EGGPlacer addresses the gap between macro-only wirelength and objectives that account for full-netlist connectivity and standard-cell density.

2 PROBLEM FORMULATION

  • The circuit is modeled as a hypergraph, and the placement task predicts movable macros’ horizontal and vertical center coordinates within the placement region.Macros must satisfy nonoverlap and boundary constraints.Source: §2 · p. 3
  • mHPWL uses macro and fixed-terminal pins, whereas full-netlist HPWL also includes standard-cell pins after placement.Both are placement-stage wirelength proxies computed without routing; omitting standard-cell connectivity and spatial demand can make mHPWL a poor indicator of mixed-size placement.Source: §2 · p. 3
  • Analytical placement combines a differentiable wirelength proxy for each net with a density penalty, capturing full-netlist connectivity and spatial competition among movable cells.λD controls the tradeoff between the wirelength and density terms.Source: §2 · p. 4
  • EGGPlacer seeks macro placements that reduce full-netlist wirelength and thermal cost while respecting macro feasibility and standard-cell spatial demand.It injects these objectives as guidance energies during reverse diffusion.Source: §2 · p. 4

3 METHOD

EGGPlacer refines denoised macro placements with composable physical and thermal energies during reverse diffusion. Analytical placement supplies standard-cell response and wirelength feedback, while a differentiable surrogate supplies temperature feedback.

3.1 ENERGY-GUIDED DIFFUSION PLACEMENT

  • At each reverse step, EGGPlacer refines the predicted clean placement using a composite energy for analytical wirelength, legality and spatial competition, and thermal behavior.The correction is incorporated into DDIM sampling, alternating denoising and physical optimization without changing the pretrained diffusion model.Source: §3.1 · pp. 4–5

3.2 ANALYTICAL PLACEMENT GUIDANCE

  • The analytical placer holds macro coordinates fixed while computing a standard-cell response, then evaluates full-netlist weighted-average wirelength with those cell coordinates treated as constants.It also marks high-occupancy standard-cell regions as obstacles; macros are jointly refined against overlap and boundary penalties.Source: §3.2 · p. 5

3.3 THERMAL GUIDANCE

  • A frozen differentiable surrogate maps macro coordinates, static geometry, macro type, and power context to per-macro temperature estimates used for thermal guidance.The objective combines an area-weighted mean with a smooth maximum; thermal guidance is bounded and reduced when placement is infeasible or conflicts with legality.Source: §3.3 · pp. 5–6
  • After reverse diffusion, a deterministic greedy legalizer moves overlapping or out-of-bounds macros to feasible grid points, processing remaining macros in descending area order.Already legal macros remain fixed, and reported EGGPlacer metrics are computed after legalization.Source: §3.3 · p. 6

4 EXPERIMENTS

Across 20 open-source designs, experiments compare macro and standard-cell-aware placement quality, runtime, end-to-end outcomes, and guidance variants. EGGPlacer achieves the lowest reported end-to-end averages, while ablations show distinct benefits from analytical and thermal guidance.

4.1 EXPERIMENTAL SETUP

  • The evaluation uses 20 ChiPBench designs, three-seed averages for EGGPlacer and ablations, and common downstream ORFS and HotSpot evaluation.DREAMPlace supplies analytical guidance; HotSpot ambient and initial temperatures are set to 318.15 K (45 °C).Source: §4.1 · pp. 6–7

4.2 PLACEMENT QUALITY AND DOWNSTREAM EVALUATION

  • EGGPlacer achieves competitive average HPWLDP among learning-based placers, closely matching RollPlace and outperforming FlowPlace, while DREAMPlace obtains the lowest HPWLDP.The comparison spans 20 benchmarks; the authors note that mHPWL and HPWLDP rankings differ considerably.Source: §4.2 · p. 7, Table 1 · p. 7
  • EGGPlacer completes macro placement and mixed-size placement in 95.40 seconds, faster than EfficientPlace, ChipDiffusion, and RollPlace, while FlowPlace is faster but does not achieve correspondingly strong HPWLDP.The runtime comparison averages results across 20 benchmarks.Source: §4.2 · p. 7, Table 2 · p. 8
  • 2.18% lower routed wirelength than RollPlace and 4.90% lower peak temperature rise than ChipDiffusion; EGGPlacer also has the lowest averages across Table 3’s three metrics.The reported reductions use the strongest external baseline for each metric.Source: §4.2 · pp. 7–8, Table 3 · p. 8

4.3 ANALYSIS AND ABLATION

  • Analytical guidance yields the strongest average HPWLDP reduction, thermal guidance the strongest peak-temperature-rise reduction, and their combination reduces normalized HPWLDP by 5.1% and temperature rise by 2.0%.The complete configuration’s reductions are relative to the variant without analytical and thermal guidance.Source: §4.3 · p. 8, Figure 4 · p. 9
  • HPWLORFS has stronger Spearman correlation with routed wirelength than HPWLDP, 0.918 versus 0.660, and higher pairwise rank agreement, 91.7% versus 72.5%.The comparison covers 80 observations across four guidance variants and 20 designs.Source: §4.3 · p. 9, Table 4 · p. 9

5 CONCLUSION

EGGPlacer uses diffusion with analytical-placement and thermal objectives to expose downstream physical feedback during macro generation. Across 20 open-source designs, it reports combined results in HPWL, routed wirelength, thermal performance, and runtime without retraining its diffusion backbone.

5 CONCLUSION

  • EGGPlacer exposes downstream physical objectives during macro generation, using analytical guidance for standard-cell response and full-netlist wirelength and thermal guidance for hotspot objectives.The conclusion describes the framework as energy-guided diffusion.Source: §5 · pp. 9–10
  • On 20 open-source designs, EGGPlacer reports combined results in HPWL, routed wirelength, thermal performance, and runtime without retraining its diffusion backbone.The conclusion motivates proxies aligned with the target downstream flow because HPWL fidelity can vary across placement engines.Source: §5 · pp. 9–10

AI USE STATEMENT

  • The paper reports using generative AI to assist methodology, mathematical descriptions, results presentation, editing, and code development, with the authors reviewing and validating the resulting work.The authors state that they take responsibility for the final content and artifacts.Source: AI USE STATEMENT · p. 10

A.1 OPTIMIZATION-BASED PLACEMENT

  • Optimization-based macro placement includes simulated-annealing search and analytical optimization using differentiable wirelength proxies and density constraints.The appendix describes DREAMPlace as using tensor operations and GPU acceleration for analytical placement.Source: §A.1 · p. 13

A.2 LEARNING-BASED MACRO PLACEMENT

  • Learning-based macro placers include reinforcement-learning policies, search and refinement methods, and generative diffusion or flow-matching approaches.The appendix notes that existing methods often do not directly couple generative trajectories to online analytical-placement feedback or thermal characteristics.Source: §A.2 · pp. 13–14
  • EGGPlacer evaluates physical objectives on intermediate denoised placements and uses their gradients to steer reverse diffusion, jointly exposing standard-cell placement behavior and thermal information.The appendix presents this as a response to the gap in direct online downstream feedback.Source: §A.2 · p. 14

B END-TO-END PHYSICAL DESIGN EVALUATION

The end-to-end evaluation fixes the generated macros and applies a common ORFS flow to the remaining physical-design stages. HotSpot is then used to estimate each completed design’s thermal distribution.

B END-TO-END PHYSICAL DESIGN EVALUATION

C DIFFUSION BACKBONE AND TRAINING DETAILS

EGGPlacer uses a shared frozen diffusion backbone and guides reverse sampling by refining predicted placements with physical-objective energies. Analytical guidance models standard-cell response and feasibility, while thermal guidance is gated by placement feasibility and legality conflicts.

C DIFFUSION BACKBONE AND TRAINING DETAILS

  • All variants use the same frozen 556,354-parameter diffusion checkpoint, trained on 40,000 synthetic circuits with deterministic DDIM sampling.The denoiser conditions on noisy macro centers, sizes, netlist features, fixed ports, and timestep.Source: C DIFFUSION BACKBONE AND TRAINING… · p. 14

C.1 DIFFUSION OBJECTIVE AND PREDICTED PLACEMENT GUIDANCE DERIVATION

  • A local quadratic trust region refines each predicted placement toward physical objectives before the reverse diffusion step; setting the guidance displacement to zero recovers unguided DDIM.Multiple inner steps can refine the prediction, and the implementation uses a finite optimization procedure.Source: §C.1 · p. 15

D.1 ANALYTICAL PLACEMENT GUIDANCE

  • At each reverse step, DREAMPlace updates standard cells for five Nesterov steps with macros fixed, then macro guidance evaluates full-netlist WA-WL with those cell coordinates held constant.The macro coordinates are subsequently refined jointly with the composite energy for ten Adam steps.Source: §D.1 · pp. 15–16
  • Analytical feasibility guidance adds rectangles derived from a 64 × 64 standard-cell occupancy histogram to the macro boxes before evaluating smooth pairwise overlap.Bins above 0.1 occupancy are marked; components are decomposed into rectangles, with rectangles below 0.1% of chip area discarded.Source: §D.1 · p. 15

D.2 THERMAL GUIDANCE

  • Thermal guidance uses per-macro temperature predictions in its objective, and its gate attenuates updates when placement is infeasible, legality conflicts, or sampling reaches its terminal step.The predictor’s whole-chip outputs are retained for calibration diagnostics rather than the guidance objective.Source: §D.2 · p. 16

E COMPLETE ENERGY GUIDANCE ABLATION RESULTS

The ablations show distinct wirelength and thermal effects from analytical and thermal guidance, while proxy reliability depends on the placement flow. The included appendix passages describe the thermal surrogate’s data, architecture, training objective, and optimization.

E COMPLETE ENERGY GUIDANCE ABLATION RESULTS

  • Analytical guidance substantially reduces HPWLDP and routed wirelength despite increasing mHPWL, while thermal guidance alone gives the lowest peak and p95 temperature rises.With analytical guidance also enabled, thermal guidance still improves both thermal metrics, with a smaller marginal benefit and a slight HPWLDP increase.Source: E COMPLETE ENERGY GUIDANCE ABLATION… · p. 16, Figure 5 · p. 17, Table 5 · p. 17

E.1 CORRELATION BETWEEN PLACEMENT PROXIES AND ROUTED WIRELENGTH

  • Within the four EGGPlacer variants, mHPWL has a negative Spearman correlation with routed wirelength of −0.474, whereas HPWLDP has a positive correlation of 0.660.The analysis normalizes metrics within each benchmark before computing correlations across 20 benchmarks.Source: §E.1 · pp. 17–18, Figure 6 · p. 18

E.2 ENGINE DEPENDENCE OF PLACEMENT PROXIES FOR ROUTED WIRELENGTH

  • HPWLORFS has stronger routed-wirelength association than HPWLDP: Spearman correlation is 0.918 versus 0.660, and pairwise rank agreement is 91.7% versus 72.5%.The proxies select the same best variant on 18 versus 8 of 20 benchmarks, respectively.Source: §E.2 · pp. 18–19, Table 6 · p. 18

F.1 TRAINING DATA AND TARGETS

  • The thermal surrogate uses 1,200 HotSpot placements from 20 benchmarks, including five Gaussian macro-coordinate perturbations per base placement, with design geometry and power context fixed.Macro power is scaled by 10 to create a controlled stress test of thermal constraints.Source: §F.1 · p. 19

F.2 NETWORK ARCHITECTURE

  • The thermal predictor is a Transformer over macro tokens with continuous Fourier coordinate features and separate heads for per-macro and whole-chip temperatures.It has 655,684 trainable parameters and uses no sequence-index embedding, making macro outputs permutation-equivariant and whole-chip outputs permutation-invariant.Source: §F.2 · pp. 19–20

F.3 TRAINING OBJECTIVE

  • Dense per-macro temperature supervision is intended to capture local thermal interactions, while the weighted whole-chip loss supports diagnostic calibration.The whole-chip objective emphasizes tail temperature while retaining supervision for other statistics.Source: §F.3 · p. 20

F.4 OPTIMIZATION SETTINGS

  • The predictor is trained with AdamW, validation-plateau learning-rate reduction, gradient clipping, and early stopping at the lowest validation loss.Random horizontal and vertical flips provide placement-preserving augmentation.Source: §F.4 · p. 20

F.5 SURROGATE CALIBRATION UNDER GUIDED SAMPLING

Thermal surrogate calibration worsens under joint analytical and thermal guidance, which may shift placements beyond the surrogate’s calibration region. The surrogate overestimates peak-temperature improvement in that setting.

F.5 SURROGATE CALIBRATION UNDER GUIDED SAMPLING

  • With analytical guidance present, thermal guidance increases mean absolute prediction error for peak and p95 temperature, with larger errors on 14 of 20 benchmarks.Without analytical guidance, thermal guidance reduces both errors.Source: §F.5 · p. 20, Figure 7 · p. 21
  • Under joint guidance, the surrogate predicts a 1.020 °C average peak-temperature reduction, while HotSpot measures 0.278 °C.The passage also reports a similar discrepancy for p95 temperature; the peak-temperature gap is smaller without analytical guidance.Source: §F.5 · p. 20, Figure 7 · p. 21
  • Joint analytical and thermal optimization may shift placements so the surrogate overestimates marginal tail-temperature improvement.Suggested responses include training on jointly guided placements and using uncertainty-informed or trust-region-constrained guidance.Source: §F.5 · p. 21

G EXAMPLE VISUALIZATIONS OF PLACEMENT AND THERMAL SIMULATION RESULTS

The visualizations show ORFS global placements for six methods on four representative designs and the corresponding steady-state HotSpot temperature distributions.

G EXAMPLE VISUALIZATIONS OF PLACEMENT AND THERMAL SIMULATION RESULTS

H COMPLETE BASELINE RESULTS FOR EACH DESIGN

The section reports per-design mixed-size placement and end-to-end results, with separate tables for mHPWL, refined HPWLDP, routed wirelength, and HotSpot peak temperature.

H COMPLETE BASELINE RESULTS FOR EACH DESIGN

I DETAILED EXPERIMENT METRICS

Table 11 presents unnormalized per-design results for four energy-guidance variants, averaged over three seeds, with a continuation table.

I DETAILED EXPERIMENT METRICS

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